Question

In the wake of a spike in criminal activity, you decide to dress up like a giant bat and help restore order to your hometown. Driving around in your tanked-up car, you notice a truck as it is just leaving (~v0 = 0 m/s) the loading bay of a shady, nefarious industrial chemical company. Upon scanning the truck, you determine that it is remote-controlled and holds a bomb whose timer will be triggered once the truck crosses the parking lot entrance 200 m away. Your integrated motion detector measures the truck’s acceleration to be 5 m/s2 towards you as you drive through the parking lot entrance toward the truck with an initial velocity of 20 m/s. Your car’s mass is a third of the truck’s (excluding you, who plans to eject at the last second).

a. What minimum acceleration should you program your car/tank in order to ensure the truck stops following the inelastic collision? Assume the collision destroys both engines so neither vehicle can accelerate afterwards.

b. Should you also account for your ejection? In other words, will the ejection change the speed of your car/tank? Explain why or why not.

Answer 1

Yes, the speed will change because the mass of system (car/you) varies before collision, so it makes more difficult the situation. For that reason, i mentioned the m2f=n. I solved the exercise assuming the case final speed are the same, but also i write the general equation.